## Tuesday, May 17, 2011

### Packing Socks in the Dark

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In your bedroom you have a drawer with 2 red, 4 yellow, 6 purple, 8 brown, 10 white, 12 green, 14 black, 16 blue, 18 grey, and 20 orange socks. The socks are all jumbled together in the drawer. It is dark in your bedroom, your partner is still asleep and so you don't want to turn on the light to see. So you cannot see which sock is which in the dark.

You are packing for a trip that will take you three days, so you need three pairs of socks.

How many socks do you need to take out to be sure that you have at least three pairs of socks of the same color?

1. I believe that you need 15 socks. The reason is that there are 10 types of socks, so if we assume that if you take 10 socks and none of them match then the 11th sock will have a match, and thus we have 9 unmatched socks. Then you need two more to make sure you have a pair and so on. So to have 3 pairs you need 15 socks.

2. minimum 13 +2 socks need to be removed to get
3 pairs as der are 10colors minimum 11 is required for one pair and if you remove two more posibly the two belong to color other than pair formed its 13 else if both belong to diff color den 2 more i.e 15 need to be removed

3. Answer is 47 to GUARANTEE you get 3 matching pairs. With (extremely) bad luck, the first 38 socks you pick could all be either orange or grey (20+18). After that you could pick 1 of each of the other colors before matching one of them (8 total). After that any of the socks left will match one of the other 8. So the answer is 20+18+9 = 47...

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